Interesting things that aren't necessarily completely obvious

[David Williams]

Each date is not equally likely to fall on each day of the week. You have the usual 28-year cycle with 21 normal years and 7 leap years, and within that everything is balanced. However, when the year ends in 00, it's only a leap year if the first 2 digits make a number that's divisible by 4. So 2000 was a leap year, but 1900 wasn't and 2100 won't be.

With 303 non leap years and 97 leap years in 400 years, that gives 146,097 days. And that number is divisible by 7. Because of that, it creates an imbalance and you get a 400-year cycle instead of a 2800-year cycle. And as 400 is not divisible by 7, it's impossible for each date to have the same probability of falling on each day of the week.

Years ago (pre-internet) I read an article about Friday 13th, which included the statement that the 13th falls on a Friday more often than any other day - without any explanation. This seemed unlikely, until I followed your logic, and realised it was possible. Faced with a long train journey, and with pencil and paper only, I decided to check it out. It's not quite as laborious as you might think. In normal times the calendar repeats every 28 years and all days are equally represented. So if you start at, say, 1/1/1901 you don't need to consider the 196 years to 31/12/2096, and you can knock out any 84 year period in both the next two centuries are well. Turns out it's true. (confirmed by Google in a second).

[Philip A]

Malabo is no longer the capital of Equitoreal Guinea! Go figure.